Gradient operators and the commensurate-incommensurate transition

In this note it is shown that gradients of bounded operators do not contribute to singularities in the bulk free energy. The formal scaling index of these operators describes at best, depending on the boundary conditions, singularities in the surface free energy. This observation is used in the context of a model, that describes the commensurate-incommensurate transition, to show that Cardy's argument for the renormalization connection of this transition with the point T=1/π of the Gaussian fixed line cannot be correct. The same model is further used to demonstrate how gradients of unbounded operators can contribute to singularities in the bulk.